DictionaryaxiomFoundational statement
noun

axiom

AK-see-um/ˈæksiəm/

A statement accepted as true as a basis for reasoning.

The proof begins with an axiom accepted throughout the mathematical system.

Represent a familiar axiom—the whole is greater than its proper part—as a compact geometric statement that two adults recognize immediately, rather than as an experiment or a worked proof.
Etymology

Greek axioma meant something thought worthy or fit, hence “authority.” This connects an axiom’s self-evident truth with its standing as a statement worthy of acceptance.

In context

Enhanced Public Domain213:28
it is an axiom admitted by all economists that peace without and peace within are necessary for the progress of Commerce and Industry
1900s Satire Audiobook: Anatole France - Penguin Island

More examples

  • Different geometries can be built from different axioms.
  • She challenged the familiar axiom that bigger is always better.
  • An axiom provides a starting point rather than a conclusion.

Forms

axiom · axioms

axiomatic adjective — Accepted as a basic truth without proof.

Similar words

postulate
Often means a basic assumption explicitly proposed for a system.
theorem
Is established by reasoning from assumptions rather than accepted initially.